Abstract
The Positivity Theorems 6.22 and 6.24 allow to apply the Stability Criterion 4.25 and the Ampleness Criterion 4.33 to the Hilbert schemes H constructed in 1.46 and 1.52 for the moduli functors C and 𝔐, respectively. We start by defining the action of the group G = Sl(l + 1, k) or G = Sl(l + 1, k) × Sl(m + 1, k) on H and by constructing G-linearized sheaves. We recall the proof that a geometric quotient of H by G, whenever it exists, is a coarse moduli scheme and we choose candidates for ample invertible sheaves on it.
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© 1995 Springer-Verlag Berlin Heidelberg
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Viehweg, E. (1995). Geometric Invariant Theory on Hilbert Schemes. In: Quasi-projective Moduli for Polarized Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79745-3_8
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DOI: https://doi.org/10.1007/978-3-642-79745-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-79747-7
Online ISBN: 978-3-642-79745-3
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